Secor wt17: Difference between revisions

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This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]''~~. (The reasoning behind this temperament is also stated in there, but maybe we should copy it here?)~~

This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'':

Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

''The requirements for a temperament having an irregular closed circle of fifths in 17... are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios. For example, ...6 system degrees of 17-ET (6º17) falls between 11:14 and 7:9. In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle. The objective is to construct the temperament in such a way that the best approximations of these ratios will occur, in the desired keys, simultaneously in chords in which these intervals (or their inversions) are used in combination, e.g., ...7:9:11 in 17.''

''In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones).... While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best 6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.''

Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

== Scala file ==

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-This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]''. (The reasoning behind this temperament is also stated in there, but maybe we should copy it here?)
+This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'':
-Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.
+''The requirements for a temperament having an irregular closed circle of fifths in 17... are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios.  For example, ...6 system degrees of 17-ET (6º17) falls between 11:14 and 7:9.  In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle.  The objective is to construct the temperament in such a  way  that  the  best  approximations  of  these  ratios  will  occur,  in  the  desired  keys,  simultaneously  in  chords  in  which  these  intervals  (or  their  inversions)  are  used  in  combination, e.g., ...7:9:11 in 17.''
+''In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones).... While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best  6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.''
+Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.
 == Scala file ==